Activity coefficient NRTL model

Fig. 4.9 also contains results from a thermodynamic consistent model of the studied esterification. The activity coefficients were modeled on the basis of phase equilibrium data alone using the NRTL equation. With that model the number for the thermodynamic equilibrium constant K of the studied esterification at 80 °C was determined from a fit to the experimental data shown in Fig. 4.9 to be... 

Blanco et al. have also correlated the results with the van Laar, Wilson, NRTL and UNIQUAC activity coefficient models and found all of them able to describe the observed phase behavior. The value of the parameter ai2 in the NRTL model was set equal to 0.3. The estimated parameters were reported in Table 10 of the above reference. Using the data of Table 15.7 estimate the binary parameters in the Wislon, NRTL and UNIQUAC models. The objective function to be minimized is given by Equation 15.11. 

A model is needed to calculate liquid-liquid equilibrium for the activity coefficient from Equation 4.67. Both the NRTL and UNIQUAC equations can be used to predict liquid-liquid equilibrium. Note that the Wilson equation is not applicable to liquid-liquid equilibrium and, therefore, also not applicable to vapor-liquid-liquid equilibrium. Parameters from the NRTL and UNIQUAC equations can be correlated from vapor-liquid equilibrium data6 or liquid-liquid equilibrium data9,10. The UNIFAC method can be used to predict liquid-liquid equilibrium from the molecular structures of the components in the mixture3. 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

The non-random two-liquid segment activity coefficient model is a recent development of Chen and Song at Aspen Technology, Inc., [1], It is derived from the polymer NRTL model of Chen [26], which in turn is developed from the original NRTL model of Renon and Prausznitz [27]. The NRTL-SAC model is proposed in support of pharmaceutical and fine chemicals process and product design, for the qualitative tasks of solvent selection and the first approximation of phase equilibrium behavior in vapour liquid and liquid systems, where dissolved or solid phase pharmaceutical solutes are present. The application of NRTL-SAC is demonstrated here with a case study on the active pharmaceutical intermediate Cimetidine, and the design of a suitable crystallization process. 

A predicted solubility curve for Cimetidine in Ethanol is shown in Figure 18. The affect of temperature on solubility occurs through two mechanisms the ideal solubility effect (Eq. 3), and the temperature dependence of the activity coefficient, y. The second affect is not correlated by the NRTL-SAC model, however it is generally accepted that in most phase equilibria problems the affect of temperature on the activity coefficient is relatively small compared to the affect on ideal solubility. A further degree of caution should be applied when extrapolating in this manner, until experimental data are collected. 

For the purpose of this case study we will select Isopropyl alcohol as the crystallization solvent and assume that the NRTL-SAC solubility curve for Form A has been confirmed as reasonably accurate in the laboratory. If experimental solubility data is measured in IPA then it can be fitted to a more accurate (but non predictive) thermodynamic model such as NRTL or UNIQUAC at this point, taking care with analysis of the solid phase in equilibrium. As the activity coefficient model only relates to species in the liquid phase we can use the same model with each different set of AHm and Tm data to calculate the solubility of the other polymorphs of Cimetidine, as shown in Figure 21. True polymorphs only differ from each other in the solid phase and are otherwise chemically identical. 

Solubility modelling with activity coefficient methods is an under-utilized tool in the pharmaceutical sector. Within the last few years there have been several new developments that have increased the capabilities of these techniques. The NRTL-SAC model is a flexible new addition to the predictive armory and new software that facilitates local fitting of UNIFAC groups for Pharmaceutical molecules offers an interesting alternative. Quantum chemistry approaches like COSMO-RS [25] and COSMO-SAC [26] may allow realistic ab-initio calculations to be performed, although computational requirements are still restrictive in many corporate environments. Solubility modelling has an important role to play in the efficient development and fundamental understanding of pharmaceutical crystallization processes. The application of these methods to industrially relevant problems, and the development of new... 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

For most of the systems with alcohols, the description of SLE was given by the average standard mean deviation (oj) < 2 K for UNIQUAC ASM and NRTL 1 equations. The procedure of correlation has been described in many articles [52-54,79,84-88,91-94]. Using GE models the solute activity coefficients in the saturated solution, y, were described. 

The solute activity coefficients, pj, of the saturated solutions were correlated for many mixtures by the NRTL model describing the excess Gibbs energy [140]... 

Belveze, L.S., Brennecke, J.F., and Stadtherr, M.A., Modeling of activity coefficients of aqueous solutions of quaternary ammonium salts with the electrolyte-NRTL equation, Ind. Eng. Chem. Res., 43, 815, 2004. 

Although COSMO-RS generally provides good predictions of chemical potentials and activity coefficients of molecules in liquids, its accuracy in many cases is not sufficient for the simulation of chemical processes and plants, because even small deviations can have large effects on the behavior of a complex process. Therefore, the chemical engineer typically prefers to use empirical thermodynamic models, such as the UNIQUAC and NRTL, for the description of liquid-phase activity coefficients with... 

As a typical example from industrial practice we consider the simulation of a process with the reaction of methylphosphinic acid and butanol to methylphosphinic acid butyl ester and water, which was modeled by Gordana Hofmann-Jovic at InfraServ Knapsack [C28]. Because of the lack of experimental data for the binary systems with phosphorous compounds, COSMO-RS was used for the prediction of the binary activity coefficients. Then the results were fitted by an NRTL equation and the entire process was modeled by a commercial process simulator. The resulting phase diagrams were in close agreement with experimental measurements obtained later (Fig. 8.2). 

Experimental studies were carried out to derive correlations for mass transfer coefficients, reaction kinetics, liquid holdup, and pressure drop for the packing MULTIPAK (35). Suitable correlations for ROMBOPAK 6M are taken from Refs. 90 and 196. The nonideal thermodynamic behavior of the investigated multicomponent system was described by the NRTL model for activity coefficients concerning nonidealities caused by the dimerisation (see Ref. 72). 

Physical property data for many of the key components used in the simulation for the ethanol-from-lignocellulose process are not available in the standard ASPEN-Plus property databases (11). Indeed, many of the properties necessary to successfully simulate this process are not available in the standard biomass literature. The physical properties required by ASPEN-Plus are calculated from fundamental properties such as liquid, vapor, and solid enthalpies and density. In general, because of the need to distill ethanol and to handle dissolved gases, the standard nonrandom two-liquid (NRTL) or renon route is used. This route, which includes the NRTL liquid activity coefficient model, Henry s law for the dissolved gases, and Redlich-Kwong-Soave equation of state for the vapor phase, is used to calculate properties for components in the liquid and vapor phases. It also uses the ideal gas at 25°C as the standard reference state, thus requiring the heat of formation at these conditions. 

The LCM is a semi-theoretical model with a minimum number of adjustable parameters and is based on the Non-Random Two Liquid (NRTL) model for nonelectrolytes (20). The LCM does not have the inherent drawbacks of virial-expansion type equations as the modified Pitzer, and it proved to be more accurate than the Bromley method. Some advantages of the LCM are that the binary parameters are well defined, have weak temperature dependence, and can be regressed from various thermodynamic data sources. Additionally, the LCM does not require ion-pair equilibria to correct for activity coefficient prediction at higher ionic strengths. Thus, the LCM avoids defining, and ultimately solving, ion-pair activity coefficients and equilibrium expressions necessary in the Davies technique. Overall, the LCM appears to be the most suitable activity coefficient technique for aqueous solutions used in FGD hence, a data base and methods to use the LCM were developed. 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

Modern theoretical developments in the molecular thermodynamics of liquid-solution behavior are based on the concept of local composition. Within a liquid solution, local compositions, different from the overall mixture composition, are presumed to account for the short-range order and nonrandom molecular orientations that result from differences in molecular size and intermolecular forces. The concept was introduced by G. M. Wilson in 1964 with the publication of a model of solution behavior since known as the Wilson equation. The success of this equation in the correlation of VLE data prompted the development of alternative local-composition models, most notably the NRTL (Non-Random-Two Liquid) equation of Renon and Prausnitz and the UNIQUAC (UNIversal QUAsi-Chemical) equation of Abrams and Prausnitz. A further significant development, based on the UNIQUAC equation, is the UNIFAC method,tt in which activity coefficients are calculated from contributions of the various groups making up the molecules of a solution. 

In order to correlate the results obtained, a modified SRK equation of state with Huron-Vidal mixing rules was used. Details about the model are reported in the paper by Soave et al. [16]. This approach is particularly adequated when experimental values of the critical temperature and pressure are not available as it was the case for limonene and linalool. Note that the flexibility of the thermodynamic model to reproduce high-pressure vapor-liquid equilibrium data is ensured by the use of the Huron-Vidal mixing rules and a NRTL activity coefficient model at infinite pressures. Calculation results are reported as continuous curves in figure 2 for the C02-linalool system and in figure 3 for C02-limonene. Note that the same parameters values were used to correlated the data of C02-limonene at 45, 50 e 60 °C. 

We can estimate the activity coefficients by using the excess Gibbs energy models. Based on the local composition concept, the Wilson, NRTL, and UNIQUAC models for excess Gibbs energy provide relations for activity coefficient... 

At atmospheric pressure, the n-butanol-water system exhibits a minimum boiling azeotrope and partial miscibility, and hence a binary heterogeneous azeotrope. Figure 1.8 shows the Tyx and Pyx phase diagrams for l-propanol(l)-water(2) azeotropic mixture obtained from the Aspen Plus simulator using the NRTL activity coefficient model. 

Next, we specify the x, between 0 and 1, and estimate the total pressure P and yx from Eq. (1.193) to prepare the total pressure and equilibrium compositions shown in Table 1.10. In Figure 1.9, we can compare both the Tyx and Pyx diagrams obtained from Raoult s law and the NRTL model using the Aspen Plus simulator. As we see, ideal behavior does not represent the actual behavior of the acetone-water mixture, and hence we should take into account the nonideal behavior of the liquid phase by using an activity coefficient model. 

Example 4.32 Column grand composite curves in methanol plant Table 4.16 describes the existing base case operations for columns 1 and 2 of the methanol plant obtained from the converged simulations using the RKS equation of state to estimate the vapor properties. The activity coefficient model, NRTL, and Henry components method are used for predicting the equilibrium and liquid properties. 

The activity coefficients of nonideal mixtures can be calculated using the molecular models of NRTL, UNIQUAC, or the group contribution method of UNIFAC with temperature-dependent parameters, since nonideality may be a strong function of temperature and composition. The Maxwell-Stefan diffusivity for a binary mixture of water-ethanol can be considered independent of the concentration of the mixture at around 40°C. However, for temperatures above 60°C, deviation from the ideal behavior increases, and the Maxwell-Stefan diffusivity can no longer be approximated as concentration independent. For highly nonideal mixtures, one should consider the concentration dependence of the diffusivities. 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

Since the degree of coupling is directly proportional to the product Q (D/k)in, the error level of the predictions of q is mainly related to the reported error levels of Q values. The polynomial fits to the thermal conductivity, mass diifusivity, and heat of transport for the alkanes in chloroform and in carbon tetrachloride are given in Tables C1-C6 in Appendix C. The thermal conductivity for the hexane-carbon tetrachloride mixture has been predicted by the local composition model NRTL. The various activity coefficient models with the data given in DECHEMA series may be used to estimate the thermodynamic factors. However, it should be noted that the thermodynamic factors obtained from various molecular models as well as from two sets of parameters of the same model might be different. 

The fugacity coefficient is usually obtained by solving an equation of state (e.g., Peng-Robinson Redlich-Kwong). The activity coefficient is obtained from a liquid phase activity model such as Wilson or NRTL (see Walas, 1985). 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

According to the NRTL model, the activity coefficients can be expressed as ... 

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